What is the rate of change of the function

Answer:

The possible arrangement= 18 ways

Step-by-step explanation:

Six identical coin are tossed.

Coin has only a tail and a head.

In how many possible ways can the arrangement be 3 head and 3 tail.

The possible arrangement= (3! * 3!)/2

The reason for dividing by two because coin has two face.

The possible arrangement= (3! * 3!)/2

The possible arrangement=( 6*6)/2

The possible arrangement= 36/2

The possible arrangement= 18 ways

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

Perimeter = 128 feet

The width is 24 feet less than the length is written as

w = l - 24

128 = 2l + 2( l - 24)

128 = 2l + 2l - 48

Group like terms

4l = 176

Divide both sides by 4

l = 44

The length is 44 feet

Substitute l = 44 into w = l - 24

w = 44 - 24

w = 20

The width is 20 feet

Hope this helps you

Answer:

[tex]\displaystyle b = 5[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^b_1 {5x + 7} \, dx = 88[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:5

Step-by-step explanation:

got it right

Answer:

D. Obtuse

Step-by-step explanation:

Answer:

You typed that incorrectly.  That first angle should be 113 degrees.

It would be an obtuse triangle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]

To divide by a fraction, multiply the reciprocal of that fraction

[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]

Reduce the number with the G.C.F 7

[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]

Reduce the numbers with the G.C.F 17

[tex] \frac{5}{6} \times \frac{3}{2} [/tex]

Reduce the numbers with the G.C.F 3

[tex] \frac{5}{2} \times \frac{1}{2} [/tex]

Multiply the fraction

[tex] \frac{5}{4} [/tex]

In mixed fraction:

[tex]1 \frac{1}{4} [/tex]

Hope this helps..

Good luck on your assignment...

Answer:

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Step-by-step explanation:

(i) probability with 16 success out of 24 = 16/24 = 2/3

(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3

Since the two experiments have the same probability, the observed probabilities are the same.

HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.

Using the binomial distribution,

(i)

p = 1/2

N = 24

x = 16 (number of successes)

P(16,24) = C(24,16) p^16* (1-p)^8

= 735471* (1/65536)*(1/256)

= 0.0438

(ii)

p = 1/2

N = 12

x = 8 (number of successes)

P(8,12) = C(12,8) p^8* (1-p)^4

= 495*1/256*1/16

= 0.1208

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Note: It would help to mention the topic you're on so answers will correspond to what is expected.  Here we cover probability and binomial distribution.

Answer:

The radius of the cylinder is 1.93mm.

Step-by-step explanation:

1) Formula to find the missing radius : V= pi r^2 (h)

( V= volume, pi=3.14 r=radius, h= height)

2) Plug all the give variables into the formula: 200=pi r^2 (17)

3) Multiply pi with 17 and then round it to the nearest hundredth which you get  53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2

4) Next you want to isolate the r^2 by dividing both sides by 53.41

200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74)  ---> 3.74=r^2

5) Now you have to square both sides to get rid of that exponent  : squared 3.74 = squared r^2

6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)

7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.

Answer:B

Step-by-step explanation:

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.

Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.

This will satisfy the requirements of the SAS theorem for considering 2 triangles to be equal or congruent.

Answer:

DEA

Step-by-step explanation:

Answer:

Step-by-step explanation:pleased to help u....

Answer:

G 10

Step-by-step explanation:

2*3x+3*2x+15=135 inches

6x+6x=120 inches

12x=120 inches

x= 10 inches

Answer:

We have the measure of both angles as  55 degrees and 35 degrees

Step-by-step explanation:

We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.

We now set up an equation using the information we are given about the problem.

From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:

x =2y -15 -------- equation 1

similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:

x + y + 90 = 180

x+ y = 90 ------------- equation 2

we can now solve the two equations simultaneously as

x -2y =-15

x+ y = 90

from this, we have that

x = 55 and y = 35

We have the measure of both angles as  55 degrees and 35 degrees

Answer:

A) Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) test statistic = -2.1226

C) p-value = 0.0598

D) Option A is correct

Step-by-step explanation:

We are given;

x = 4.52 minutes

s = 0.75 minutes

μ = 5 minutes

n = 11

degree of freedom = n - 1 = 11 - 1 = 10

A) The hypotheses are;

Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) t-statistic = (x - μ)/(s/√n)

(4.52 - 5)/(0.75/√11) = -2.1226

C) From the t-score calculator results attached, the p-value is approximately 0.0598.

D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.

Answer:

B

Step-by-step explanation:

The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have a graph.

So, slope of line in graph is

= (-1-1)/ (0.-3)

= -2/ (-3)

= 2/3

and, we know that two parallel line have same slope.

so, the slope of parallel line is 2/3 and the x intercept is -3.

So, the Equation line is y= 2/3 x  + b

0 = 2/3 (-3) +b

b= 2

Thus, the required equation is y= 2/3x + 2.

Learn more about Slope here:

https://brainly.com/question/2863474

#SPJ5

Answer:

See below

Step-by-step explanation:

The statement that can be written for 4p = 8 is:

=> Four times a certain number equals eight.

Answer:

A. [tex]x^5+C[/tex]

Step-by-step explanation:

This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -

[tex]5\cdot \int \:x^4dx[/tex]

We can then apply the power rule " [tex]\int x^adx=\frac{x^{a+1}}{a+1}[/tex] ", where a = exponent ( in this case 4 ),

[tex]5\cdot \frac{x^{4+1}}{4+1}[/tex]

From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -

[tex]5\cdot \frac{x^{4+1}}{4+1}\\[/tex] - Add the exponents,

[tex]5\cdot \frac{x^{5}}{5}[/tex] - 5 & 5 cancel each other out,

[tex]x^5[/tex] - And now adding the constant we see that our solution is option a!

Answer:

Answer A

Step-by-step explanation:

Use the property of integrals. You now have [tex]5 x\int\limits\,x^{4}dx[/tex] where the first x next to the 5 stands for multiplication. Let's evaluate it. We get [tex]5 (\frac{x^{5} }{5})[/tex]. From here, we can simplify this into [tex]x^{5}[/tex]. Add the constant of integration, which will give you the answer of [tex]x^{5} + C[/tex].

Answer:

36.1683

Step-by-step explanation:

45*80.374/100=

Answer:

-5 < x < 0

Step-by-step explanation:

Answer:

The line that is perpendicular to B has a slope of -1/2

Step-by-step explanation:

First find the slope of line B

m = ( y2-y1)/(x2-x1)

    = (10-0)/(5-0)

    = 10/5

    = 2

Lines that are perpendicular have slopes that multiply to -1

m * 2 = -1

m = -1/2

The line that is perpendicular to B has a slope of -1/2

Answer:

-1/2x

Step-by-step explanation:

Hey there! :)

Well to find the slope of line B we'll use the following formula.

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

We'll use the points (0,0) and (5,10),

10 - 0 = 10

5 - 0 = 5

Slope = 2x

The slopes of 2 perpendicular lines are reciprocals of each other,

meaning if the slope of line B is 2x then its perpendicular lines slope is -1/2x.

Hope this helps :)

====================================================

Explanation:

Triangle CDA is congruent to triangle CDB. We can use the HL (hypotenuse leg) congruence theorem to prove this. This only works because we have two right triangles.

Since CDA and CDB are congruent, this means their corresponding pieces are the same length. Specifically AD = DB, so

AD+DB = AB

AD+AD = 3

2*AD = 3

AD = 3/2 = 1.5

For triangle CDA, we have AD = 3/2 = 1.5 and CD = sqrt(3). We can use the pythagorean theorem to find the missing side AC

a^2 + b^2 = c^2

(AD)^2 + (CD)^2 = (AC)^2

(3/2)^2 + (sqrt(3))^2 = (AC)^2

9/4 + 3 = (AC)^2

(AC)^2 = 9/4 + 3

(AC)^2 = 9/4 + 12/4

(AC)^2 = 21/4

AC = sqrt(21/4)

AC = sqrt(21)/sqrt(4)

AC = sqrt(21)/2

This is the same as writing (1/2)*sqrt(21) or 0.5*sqrt(21)

Answer:

The answer is "A'' -2 because anything next to the letter x is the slope

Step-by-step explanation:

The equation to slops is y=mx+b

m= slope

b= y intercept

Slope = -2

Y intercept = ( 0 , -1)

Step-by-step explanation:

Hope this helps. Your answer would be A

Answer:

y=(x/6)

Step-by-step explanation

divide every input by 6 to get the output

Answer:

Step-by-step explanation:

First , let us rewrite the given equation into y= mx+b format

.y= -x +7

Slope is -1

Slope of the line perpendicular to the given equation is -(-1) ie., 1

Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b

1 = -1 +b

2 = b

Equation of the line perpendicular to the given equation and passing through (-1,1) is

y=x +2

Step-by-step explanation:

The amount left is:

A = A₀ (½)^(t/T)

where A₀ is the initial amount,

t is the amount of time,

and T is the half life.

a) A = 100 g (½)^(250 yr / 68.9 yr)

A = 8.09 g

b) 12.5 g = 100 g (½)^(t / 68.9 yr)

0.125 = (½)^(t / 68.9 yr)

3 = t / 68.9 yr

t = 206.7 yr

Answer:

x = -6 and x = 4

Step-by-step explanation:

In math, the critical points of a function are the points where the derivative equals zero.

So, first we will find the derivative of the function. The derivative is:

[tex]f'(x)=3x^2 +6x-72[/tex]

Now, we are going to make the derivative equal zero and find the answers of the equation.

[tex]3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\[/tex]

So we have that the critical points are the answers to this equation:

[tex]x+6= 0 \\x= - 6[/tex]

and

[tex]x-4=0\\x=4[/tex]

Thus, the critical points are x=-6 and x=4

Using it's concept, it is found that the critical numbers of the function are:

x = -6 and x = 4.

The critical numbers of a function f(x) are the values of x for which it's derivative is zero, that is:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = x^3 + 3x^2 - 72x[/tex]

The derivative is:

[tex]f^{\prime}(x) = 3x^2 + 6x - 72[/tex]

[tex]f^{\prime}(x) = 3(x^2 + 2x - 24)[/tex]

Then:

[tex]f^{\prime}(x) = 0[/tex]

[tex]3(x^2 + 2x - 24) = 0[/tex]

[tex]x^2 + 2x - 24 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = 2, c = -24[/tex], which we have to solve.

[tex]\Delta = 2^2 - 4(1)(-24) = 100[/tex]

[tex]x_{1} = \frac{-2 + \sqrt{100}}{2} = 4[/tex]

[tex]x_{2} = \frac{-2 - \sqrt{100}}{2} = -6[/tex]

The critical numbers of the function are x = 4 and x = -6.

A similar problem is given at https://brainly.com/question/16944025

Answer:

20cm it's is the answers

Step-by-step explanation:

5*4=20

Hey there! I'm happy to help!

First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).

Let's convert this below

A: (1,1)⇒(-1,-1)

B: (5,4)⇒(-5,-4)

C: (7,1)⇒(-7,-1)

D: (3,-2)⇒(-3,2)

Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.

A: (-1,-1)⇒(4,-2)

B: (-5,-4)⇒(0,-5)

C: (-7,-1)⇒(-2,-2)

D: (-3,2)⇒(2,1)

Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)

Now you know how to find the coordinates of translated figures! Have a wonderful day! :D

Answer:

The first one is correct

The second one is also correct

The third is also correct

Congrats!

Answer:

1) [tex]\boxed{Option \ B}[/tex]

2) [tex]\boxed{Option \ B}[/tex]

3) [tex]\boxed{Option \ B}[/tex]

You're totally correct, Man! :)

Step-by-step explanation:

Question 1:

[tex](6b^2-4b+3)-(9b^2-3b+6)\\Resolving \ the\ brackets\\6b^2-4b+3-9b^2+3b-6\\Combining \ like \ terms\\6b^2-9b^2-4b+3b+3-6\\-3b^3-b-3[/tex]

Question 2:

[tex](b+6)(b-3)\\Using \ FOIL\\b^2-3b+6b-18\\b^2+3b-18[/tex]

Question 3:

[tex](4x-3)(6x-1)\\Using \ FOIL\\24x^2-4x-18x+3\\24x^2-22x+3[/tex]

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation: